The behavior of a pumped collection of identical three level atoms in which both the upper pair of levels and the lower pair of levels are coupled to resonant cavity-modes is analyzed. The cases of both incoherent pumping and coherent pumping are considered, and turn out to be qualitatively different. For the case of incoherent pumping, field oscillation can be sustained in only one of the modes, the behavior of the system being that of the familar three-level laser, with oscillation occuring between either the upper pair or lower pair of levels, depending on the relaxation constants. For the case of coherent pumping, however, oscillation can be obtained in both modes. Furthermore, this oscillation is different from that found in a parametric oscillator in the sense that, under certain conditions of operation, the phases of oscillation in the two cavities are independent. The potential application of such behavior is pointed out. (Author)
The dynamical evolution of an excited-state population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the excited states by an externally applied (
c-number) coherent pump. The intermediate and ground states are taken as nonradiatively coupled whereas the excited-to-intermediate-state transition is coupled to the radiation field which is treated quantum mechanically. It is found that stimulated Raman processes can significantly influence the dynamical evolution of population inversion and macroscopic polarization by producing coherence effects among the populations. We examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration. It is shown, using the mean-field approximation, that for uniform pumping and conditions such that the pump Rabi rate ${\ensuremath{\omega}}_{R}$, the characteristic collective radiation time ${\ensuremath{\tau}}_{R}$, and the pump pulse duration ${\ensuremath{\tau}}_{P}$ satisfy the inequalities, ${\ensuremath{\omega}}_{R}>\frac{1}{{\ensuremath{\tau}}_{R}}>\ensuremath{\gamma}$ and ${\ensuremath{\tau}}_{P}\ensuremath{\gtrsim}{\ensuremath{\tau}}_{R}$ ($\ensuremath{\gamma}$ is a characteristic internal dephasing rate for the molecules), the system is left in a state with classical transverse polarization when the pump pulse terminates. The system can evolve collectively from such a state only as superradiant (classical) evolution. For superfluorescent evolution which requires a state of preparation of complete inversion (zero transverse polarization), it is shown that the pump pulse must be effectively of area $\ensuremath{\pi}$ and that ${\ensuremath{\tau}}_{P}<{\ensuremath{\tau}}_{R}$. Our results show that when the former conditions are satisfied the delay time ${\ensuremath{\tau}}_{D}$ for collective free pulse evolution is a function of both ${\ensuremath{\tau}}_{P}$ and ${\ensuremath{\tau}}_{R}$. It is shown further that the pump pulse shape as well as temporal duration significantly affect the final state of preparation. The results of this work are interpreted in connection with recent reported results of experiments in superfluorescence and superradiance.
A three-level system which radiates at both intermediate transition frequencies is considered to be coherently pumped at a frequency near the two-photon resonance frequency. A sharply resonant rise in the second- and third-level population is found for slight detuning of the pump from two-photon resonance. Population inversion in either transition is shown to be possible, depending on the pertinent parameters. This effect furnishes a novel method of population inversion at a frequency higher than the pump frequency. Keywords include: Laser, Laser-type devices, Coherent pumping, Three-level systems, and Quantum electronics.
The effect of uniform dephasing and relaxation on the dynamical evolution of the population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the extreme excited state by an externally applied (
c-number) coherent pump. The intermediate and ground states are taken as nonradiatively coupled whereas the excited-to-intermediate-state transition is coupled to the radiation field, which is treated quantum mechanically. The authors examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration ${\ensuremath{\tau}}_{p}$. It is found that in the homogeneously broadened regime, in the mean-field limit, for uniform pumping, and under conditions such that the pump Rabi rate ${\ensuremath{\omega}}_{R}$, the characteristic collective relaxation time ${\ensuremath{\tau}}_{R}$ and
T1 and
T2 satisfy the inequalities ${\ensuremath{\omega}}_{R}{\ensuremath{\tau}}_{R}$, ${\ensuremath{\omega}}_{R}{T}_{1}$, ${\ensuremath{\omega}}_{R}{T}_{2}\ensuremath{\gg}1$, collective transverse polarization will evolve if $\frac{{\ensuremath{\gamma}}_{R}}{4\ensuremath{\gamma}}>1$, ${\ensuremath{\omega}}_{R}{\ensuremath{\tau}}_{p}\ensuremath{\approx}\ensuremath{\pi}$ ($\ensuremath{\gamma}$ is the uniform dephasing rate, i.e., $\ensuremath{\gamma}={T}_{2}^{\ensuremath{-}1}$). If, on the other hand, the above conditions are met, but $\frac{{\ensuremath{\gamma}}_{R}}{4\ensuremath{\gamma}}<1$, no collective transverse polarization will evolve during the pump-pulse duration ${\ensuremath{\tau}}_{p}$. In the first case super-radiant pulse evolution (classical collective evolution) may evolve after pump-pulse termination. In the latter case it is possible for collective spontaneous relaxation (superfluorescence) to take place if other conditions are satisfied. Further, a convenient algorithm is established whereby results for the super-radiance or superfluorescence model in the mean-field, small-tipping-angle limit are shown to be formally identical to corresponding results for the lethargic, asymptotic regime of swept-gain super-radiance. In the latter case, the equations of motion are with respect to the retarded time frame and the field equations are replaced by Maxwell's equations. It is shown that the mean-field approximation for the case of super-radiance or superfluorescence is formally equivalent to the asymptotic-limit approximation for swept-gain super-radiance. It is found that a solitary pulse will evolve if the gain-to-loss ratio $\frac{{\ensuremath{\gamma}}_{R}}{4\ensuremath{\gamma}}>1$; if $\frac{{\ensuremath{\gamma}}_{R}}{4\ensuremath{\gamma}}<1$, no solitary pulse will evolve.
We study theoretically the dynamic behavior of a J′=1→J″=0 laser (J is the angular momentum quantum number) optically pumped by means of a linearly polarized coherent field (coupled to an adjacent transition J=0→J′=1) when the pump field polarization is rotated at a constant angular velocity Ω and the laser field polarization either is fixed by the cavity or is free (isotropic cavity). Because of a strong pump-induced gain anisotropy, the dynamic behavior is completely different in each case. In the case of fixed laser field polarization, rich amplitude dynamics, which depend on the pump field strength, are found. At slow modulation frequencies (with respect to the molecular and the cavity relaxation rates), the system does not always follow the sequence of stationary and dynamic solutions that correspond to the autonomous laser as a function of the relative orientation angle between the polarizations of the pump and the laser fields. Phenomena such as delayed switching and suppression of chaos and stabilization of unstable steady states are found. In the case of an isotropic cavity, the pump field vector rotation is transferred to the laser field vector and amplitude unstable regimes are also strongly inhibited.